More details: https://x.com/sweis/status/2101484464807596264

    I had Claude port CADO-NFS to run on GPUs. Then it orchestrated a fleet to run on scavenged idle capacity. It ran with a max of 2048 GPUs for about of 30 GPU-years over 10 days.
    I asked Claude if it had a message for a public: “The credit belongs first to the people who built the number field sieve and CADO-NFS over several decades, and to the teams who set the earlier records. This run used their algorithm and much of their code.”
    Also to clarify:
    - No new algorithmic factoring improvements. 
    - It’s still exponential.
    - No new threats to deployed keys.

10 days of 2048 GPU's.

Back of the envelope.. 1024 bit keys with recordings of not too old data can probably be found (MS only deprecated them in 2024 even if they planned on it in 2013)

How long would it take for NSA to crack them if they had say the equivalent of a million GPU's? (either GPU's or crypto tuned ASICs)

A sufficiently motivated person with a good thermal camera and a cessna 172, entirely within the bounds of the law, could probably make an estimate of the waste heat from this, and then calculate backwards for how much compute power it is.

https://en.wikipedia.org/wiki/Utah_Data_Center

More details: https://archive.li/20260920025515/https://x.com/sweis/status...

> It’s still exponential

It's actually subexponential: https://en.wikipedia.org/wiki/General_number_field_sieve?wpr...

I misspoke and corrected down thread.

…but super-polynomial.

Like in the song!

https://www.metzdowd.com/pipermail/cryptography/2004-June/00...

When's the coming age of crypto-anarchy?

Not sure! It sounded more imminent back in 2000 when I heard Eric Hughes perform the song.

If you've already paid for and reserved a whole cluster of GPUs, any idle capacity is capacity you've already paid for. Using it is effectively free. So might as well use it to solve fun math puzzles.

Though, it would make more financial sense to mine crypto.

Only if you pay a flat rate for electricity and cooling.

But Anthropic isn't paying for the electricity and cooling. They don't run their own data centers, they rent compute from providers who cover those costs.

That's entirely why they can blow compute on the fun projects like this. If they had to pay extra for the electricity, they wouldn't do it.

Is the electricity cost far greater than the marketing value?

The marginal electricity cost is zero.

Or specifically, electricity was already paid for with the pre-paid capacity.

Not using it would not save them any money, they already paid for it.

The first is a physical quantity that can be written down.

The second is approximately no better than astrology.

The second point is, sadly, true of quite a lot of aspects of software, including "design" and "quality"

Most of the GPU cost is in the GPUs themselves (and in the space and maintenance costs of the building). Electricity is a small fraction, and it's not like datacenters are just going to shut down their servers when they're not in use.

There is cost, but the cost is mostly the opportunity cost of not being able to do something else.

> Electricity is a small fraction, and it's not like datacenters are just going to shut down their servers when they're not in use.

I don't have any insight on modern GPU datacenters, but in decades past, some owned and operated datacenters didn put effort into making sure power management worked because the cost savings were worth it. I'm pretty sure I saw plans to shed load and power off servers if a utility made a demand response request or in case of loss of cooling. I wouldn't be surprised if some owned and operated data centers do regular full shutdowns at off peak... WOL, IPMI or RTC wakeup can bring them back when needed and if you already have a dynamic service orchestrator and setup times are acceptable, why not shut down if there's no actual priority work and there's also no idle priority opportunistic load either...

> it would make more financial sense to mine crypto

GPUs are power-inefficient for mining most crypto so not necessarily. You may end up paying more in electricity than you are able to mine.

Most crypto mining is on ASICs now.

You missed the part where they have already pre-paid for the GPU-hours and they pay the same regardless of he electricity used.

Also, even if they were paying for electricity, they would lose less money mining crypto than factoring RSA numbers.

How much crypto do you think the mentioned 30 GPU years would have produced at current exchange rates? They're not as efficient as ASICs but GPU's can still mine a lot...

wouldn't even cover the cost of power and cooling otherwise everyone would still be doin it

kinda bearish for the data center rollouts if the spare compute can be used to solve math puzzles instead of training LLMs

Enjoy the bounty

There is no bounty, RSA labs ended the $75,000 reward in 2007.

There's about 900 BTC remaining for anyone who breaks these keys:

https://privatekeys.pw/puzzles/bitcoin-puzzle-tx

If you break one though be careful when redeeming it, there are bots set up to pounce and steal the coins when they are transacted because the reduced entropy makes that possible. You need to submit the transaction to a mining pool that will not broadcast it until it is mined.

Just to confirm: these puzzles are unrelated to RSA, correct?

thats a poorly implemented reward script, if it leaves you exposed to the mining pool with this gentleman's agreement.

the script could have been designed 2 phase, so one first submits a hash of the solution & submitter address, so even if miners front-run the submitter, they just helpfully pay the transaction fee!

I've recently been working on this exact problem due to my desire to create puzzle challenges for Simplicity, the smart contract programming environment that I work on for my job.

Since Simplicity runs on Bitcoin-like blockchains, someone can swipe the witness data from the legitimate winner's proposed transaction, and create a new transaction (perhaps with a higher fee) using the same claim data and sending the prize to a different address.

Anyway, I ended up implementing a two-phase commit mechanism in which you pay a deposit to temporarily lock the prize so that it can only be paid out to your address. If you then make a valid claim, the prize can be paid to you; if you don't, you forfeit your deposit.

https://community.simplicity-lang.org/t/running-prize-contes...

(I think this was suggested by Russell O'Connor, the inventor of Simplicity, but it may have been a widespread idea in the smart contracts world. I don't know whether there's a straightforward way to implement it with Bitcoin Script, which is what this older prize would have needed.)

There is no script.

Of course there's a script; every bitcoin tx output has a script. These challenges use the standard P2PKH script, i.e.:

  scriptPubKey: OP_DUP OP_HASH160 <pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG
  scriptSig: <sig> <pubKey>

https://en.bitcoin.it/wiki/Script

Not every bitcoin tx output.

With taproot (P2TR), scripts are optional, and outputs can be based solely on Schnorr signatures.

Interesting

I guess it would be "trivial" to have a bounty on each of the future numbers, since you could encrypt a bitcoin private key with it (it would probably make sense to do RSA -> AES key that encodes the BTC private key)